Question

Let f(x)=cos(pi*x/3)
g(x)=1^x+(−1)^x
h(x)=f(x)⋅g(x)
where x is a positive integer.

Given that h(x) has a range of exactly 3 different values: a, b and c,
what is the value of a^2+b^2+c^2?

Answer 1

for successive values of
g(x) = 0 if x is odd
g(x) = 2 if x is even

f(x) = 1/2 if x = 1,5,9,...
f(x) = -1/2 if x = 2,4,8,10,...

x f g
1 1/2 0
2 -1/2 2
3 -1 0
4 -1/2 2
5 1/2 0
6 1 2
This repeats, so fg has the values 0,1,-1

a^2+b^2+c^2 = 2

Answer 2

sory sir, but it says incorrect